【摘要】：首先,簡述了復雜網(wǎng)絡,時滯系統(tǒng),分岔和多智能體系統(tǒng)的基本概念、研究背景和研究意義以及本論文的主要內容和創(chuàng)新性工作。其次,考慮了兩種時滯神經(jīng)網(wǎng)絡的Hopf分岔問題,一種是含有七個神經(jīng)元和七個時滯的BAM神經(jīng)網(wǎng)絡,另一種是含有2n個神經(jīng)元的神經(jīng)網(wǎng)絡。這兩種模型都是第一次被分析,對豐富和促進神經(jīng)網(wǎng)絡的發(fā)展具有一定的意義。另外,由于它們都含有較多的神經(jīng)元和較多的時滯,所以它們更加接近現(xiàn)實,更加有利于理解現(xiàn)實中的神經(jīng)網(wǎng)絡。主要研究方法是:以部分時滯的和作為分岔參數(shù),通過分析對線性化后系統(tǒng)的特征方程,獲得了使系統(tǒng)產(chǎn)生分岔的參數(shù)臨界值以及使系統(tǒng)產(chǎn)生分岔的充分條件。更深入的是,對于第一種模型,通過利用中心流形定理和正規(guī)型法則,分析了其Hopf分岔的穩(wěn)定性和方向,以及分岔周期的部分性質。然后,一類二階線性多智能體系統(tǒng)的一致性問題被分析和研究,每個智能體都有自身的速度和位置兩個變量,在設計的一致協(xié)議下,每個智能體隨著時間的推移逐漸趨于同一種狀態(tài)。隨后,線性的和非線性的兩種多智能體系統(tǒng)被分別研究。對于線性系統(tǒng),設計了一種簡化的一致性協(xié)議,該協(xié)議使得智能體之間的復雜信息交流被限制在一棵有向生成樹中。對于非線性系統(tǒng),設計了一種含有反饋增益的一致性協(xié)議,該協(xié)議使得每一個智能體的運行狀態(tài)都要受到其自身狀態(tài)的影響。通過相應的推導計算獲得了比其他某些文獻中更加優(yōu)越的一致性條件。它們的研究方法是:設計一致性協(xié)議,利用圖論和矩陣的一些性質推導計算,獲得使誤差系統(tǒng)在原點穩(wěn)定的條件。線性系統(tǒng)系數(shù)矩陣的特征值的實部是否都為負是判斷該系統(tǒng)是否穩(wěn)定的重要條件。對于非線性系統(tǒng),判斷其穩(wěn)定的主要方法是李雅普諾夫第二方法,即通過構造V函數(shù)來進行判斷。最后,對本論文所做的工作進行了總結以及對未來工作的研究方向進行了說明。
[Abstract]:Firstly, the basic concepts, research background and significance of complex networks, time-delay systems, bifurcation and multi-agent systems, as well as the main contents and innovative work of this paper are briefly introduced. Secondly, the Hopf bifurcation problem of two kinds of time-delay neural networks is considered, one is BAM neural network with seven neurons and seven delay, the other is the neural network with 2n neurons. These two models have been analyzed for the first time, which have a certain significance to enrich and promote the development of neural networks. In addition, they all contain more neurons and more time-delay, so they are closer to reality and more conducive to understanding the real-world neural network. The main research methods are as follows: taking the sum of partial delay as the bifurcation parameter, by analyzing the characteristic equation of the linearized system, the critical value of the parameter of the system and the sufficient conditions for the bifurcation of the system are obtained. Furthermore, for the first model, the stability and direction of the Hopf bifurcation and some properties of the bifurcation period are analyzed by using the central manifold theorem and the rule of normal type. Then, the consistency problem of a class of second-order linear multi-agent systems is analyzed and studied. Each agent has its own two variables of speed and position. Each agent gradually tends to the same state over time. Subsequently, two kinds of multi-agent systems, linear and nonlinear, are studied respectively. For linear systems, a simplified consistency protocol is designed, which limits the communication of complex information between agents to a directed spanning tree. For nonlinear systems, a consistency protocol with feedback gain is designed, which makes the operation state of each agent affected by its own state. Through the corresponding derivation and calculation, better consistency conditions are obtained than those in some other literatures. Their research methods are as follows: the consistency protocol is designed, some properties of graph theory and matrix are used to derive and calculate, and the conditions to make the error system stable at the origin are obtained. Whether the real part of the coefficient matrix of a linear system is negative or not is an important condition to determine whether the system is stable or not. For nonlinear systems, the main method for judging the stability of nonlinear systems is Lyapunov's second method, that is, by constructing a V function to judge the stability of nonlinear systems. Finally, the work of this paper is summarized and the research direction of the future work is explained.
【學位授予單位】：青島科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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相關期刊論文 前1條

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本文編號：2434713